首页 > ACM题库 > HDU-杭电 > HDU 1014 Uniform Generator-模拟-[解题报告] C++
2013
11-26

HDU 1014 Uniform Generator-模拟-[解题报告] C++

Uniform Generator

问题描述 :

Computer simulations often require random numbers. One way to generate pseudo-random numbers is via a function of the form

seed(x+1) = [seed(x) + STEP] % MOD

where ‘%’ is the modulus operator.

Such a function will generate pseudo-random numbers (seed) between 0 and MOD-1. One problem with functions of this form is that they will always generate the same pattern over and over. In order to minimize this effect, selecting the STEP and MOD values carefully can result in a uniform distribution of all values between (and including) 0 and MOD-1.

For example, if STEP = 3 and MOD = 5, the function will generate the series of pseudo-random numbers 0, 3, 1, 4, 2 in a repeating cycle. In this example, all of the numbers between and including 0 and MOD-1 will be generated every MOD iterations of the function. Note that by the nature of the function to generate the same seed(x+1) every time seed(x) occurs means that if a function will generate all the numbers between 0 and MOD-1, it will generate pseudo-random numbers uniformly with every MOD iterations.

If STEP = 15 and MOD = 20, the function generates the series 0, 15, 10, 5 (or any other repeating series if the initial seed is other than 0). This is a poor selection of STEP and MOD because no initial seed will generate all of the numbers from 0 and MOD-1.

Your program will determine if choices of STEP and MOD will generate a uniform distribution of pseudo-random numbers.

输入:

Each line of input will contain a pair of integers for STEP and MOD in that order (1 <= STEP, MOD <= 100000).

输出:

For each line of input, your program should print the STEP value right- justified in columns 1 through 10, the MOD value right-justified in columns 11 through 20 and either "Good Choice" or "Bad Choice" left-justified starting in column 25. The "Good Choice" message should be printed when the selection of STEP and MOD will generate all the numbers between and including 0 and MOD-1 when MOD numbers are generated. Otherwise, your program should print the message "Bad Choice". After each output test set, your program should print exactly one blank line.

样例输入:

3 5
15 20
63923 99999

样例输出:

         3         5    Good Choice

        15        20    Bad Choice

     63923     99999    Good Choice

解题报告:

题目大意:有一个可以产生从0到mod-1的范围的随机数的公式是seed(x+1) = [seed(x) + STEP] % MOD,seed(1)=0,利用这个公式产生的随机数可能有mod-1个不同的,也可能少于这么多,给定一个STEP和一个MOD,若对于这一对你数,可以产生mod-1个不同的随机数,则称这个是一个Good Choice否则为Bad Chioce,还有就是注意一下输出的格式。

模拟题,定义一个数组,标记产生的这个随机数是不是已经产生过了,若这个随机数是已经产生过的,那么接下来就会进入一个周期,这样的话随机数就达不到mod-1个了。

1 #include<cstdio>
 2 #include<cstring>
 3 int visit[100005];
 4 int main() {
 5     int step,mod,front;
 6     while(scanf("%d%d",&step,&mod)!=EOF) {
 7         memset(visit,0,sizeof(visit));
 8         visit[0]=1;
 9         front=0;
10         int i;
11         for(i=1;i<mod;++i) {
12             front=(front+step)%mod;
13             if(visit[front])
14             break;
15             visit[front]=1;
16         }
17         if(i==mod)
18         printf("%10d%10d    Good Choice\n\n",step,mod);
19         else
20         printf("%10d%10d    Bad Choice\n\n",step,mod);
21     }
22     return 0;
23 }